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# Congruence and Residues

+1
189
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Remove the integers which are congruent to 3 (mod 7) from the following list of five integers, and sum the integers that remain.$$85 \qquad 49,\!479 \qquad -67 \qquad 12,\!000,\!003 \qquad -3$$

May 11, 2020

#1
+2

85 mod 7 =1 Keep

49,479 mod 7 = 3 Remove

-67 mod 7 =3 Remove

12,000,003 mod 7 =1 Keep

-3 mod 7 = 4 Keep

[85 +12,000,003 - 3] =12,000,085

May 11, 2020
#2
+111566
+2

There is more than one answer for this.

for instance:

-3 mod 7 does equal -3 but it also equals 4.  Which one do you want?

Maybe it is mod 7 of the result that is wanted. In which case there would be only one answer.

Melody  May 11, 2020